\chapter{Security Analysis}
Informally, the security of aggregated signature schemes is equivalent to non-existence of an adversary capable, within the confines of a certain game, of existentially forging the aggregate signature $\cite{boneh2003aggregate}$.
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Eavesdropper aiming to forge the aggregated signature goes in vain as aggregated scheme poses a lot of limitations to get anything after peeping into the communication channel. Security Analysis analyzes the reliability of Structural Authentication Scheme in two major prospective i.e. Authenticity and Leakage. 

\section{Authenticity} The considered technical report states that any violation to content or structure of the tree can be easily detected using this structural authentication scheme. They claim that this scheme is safeguarded by adaptive chosen cipher text attack also known as CCA2 \cite{wiki:ciph}. In this attack, eavesdropper sends a number of messages to be encrypted and then use the results to explore the secret key. In structural authentication scheme this cannot happen as it falls under the strong RSA assumption of CRSA and also in BGLS it is assumed hard according to Computational co-DHP. As according to our scheme it is infeasible to compute aX \cite{kundustructural}. It focuses on a fact that if someone is capable of contaminating the content or structural position of any node than this will raise questions about the used hash function $\mathcal{H}$. Otherwise RSA or BGLS is not secure which leads to utter absurdity. 
	
\section{Leakage} Structural Authentication Scheme makes use of randomized ordered numbers which make it leakage free because for instance if subtree is shared with a user and he has access to some nodes, even if some nodes are in between and are un shared, He cannot predict their RRON, RPON or RION. This is because of their generation through a random sequence.
In comparison with MHT, structural authentication scheme ensures authentication and confidentiality, so it is more secure to be employed over high security network channels.
 
